It would be the same burden. You're still using the same dumbbell, you're just working one arm at a time instead of two.
While it's the same amount of mass, the distribution of force on your body will change as will the muscles engaged etc. no?
The mass would halve, because you are now only lifting one dumbbell with one arm instead of two dumbbells with two arms.
The issue at hand I believe is how the descent of your lift (eccentric muscle contraction) is more beneficial than the opposite, so to optimise for this you'd lift one dumbbell with two arms and then bring it down with one (i.e. minimise the effort required to lift, maximise effort required to descend).